Name ______________________________________________________
Date ___________________
Complete the following two-column proofs.
Proof #1:
A
B
D
C
̅̅̅̅; 𝐴𝐷
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
Given: ̅̅̅̅
𝐴𝐵 ≅ 𝐶𝐷
Prove: ∠𝐴 ≅ ∠𝐶
Statements
Reasons
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ ; 𝐴𝐷
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
1. 𝐴𝐵
_______________________________________
̅̅̅̅ ≅ 𝐵𝐷
̅̅̅̅
2. 𝐵𝐷
_______________________________________
3. ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵
_______________________________________
4. ∠𝐴 ≅ ∠𝐶
_______________________________________
M
Proof #2:
O
T
̅̅̅̅; 𝑂𝑇
̅̅̅̅ bisects ∠𝑀𝑇𝐴
Given: ̅̅̅̅̅
𝑀𝑇 ≅ 𝑇𝐴
Prove: ∠𝑀 ≅ ∠𝐴
Statements
A
Reasons
̅̅̅̅; 𝑂𝑇
̅̅̅̅ bisects ∠𝑀𝑇𝐴
̅̅̅̅̅ ≅ 𝑇𝐴
1. 𝑀𝑇
_______________________________________
2. ∠𝑀𝑇𝑂 ≅ ∠𝐴𝑇𝑂
_______________________________________
3. ___________________________________
Reflexive property (same line)
4. ∆𝑀𝑇𝑂 ≅ ∆𝐴𝑇𝑂
_______________________________________
5. ∠𝑀 ≅ ∠𝐴
_______________________________________
R
Proof #3:
F
O
̅̅̅̅
Given: ∠𝑅 ≅ ∠𝑆; O is the midpoint of 𝑅𝑆
̅̅̅̅
Prove: O is the midpoint of 𝐹𝑇
T
S
Statements
Reasons
1. ∠𝑅 ≅ ∠𝑆; O is the midpoint of ̅̅̅̅
𝑅𝑆
_______________________________________
2. ___________________________________
Definition of midpoint
3. ∠𝑅𝑂𝐹 ≅ ∠𝑆𝑂𝑇
_______________________________________
4. ∆𝐹𝑅𝑂 ≅ ∆𝑇𝑆𝑂
_______________________________________
̅̅̅̅
5. ̅̅̅̅
𝐹𝑂 ≅ 𝑂𝑇
_______________________________________
6. O is the midpoint of ̅̅̅̅
𝐹𝑇
_______________________________________
Proof #4:
S
N
O
W
Reasons
Given: ∠𝑆 ≅ ∠𝑂; ̅̅̅̅
𝑆𝑂 ⊥ ̅̅̅̅̅
𝑁𝑊
̅̅̅̅̅
̅̅̅̅̅
Prove: 𝑆𝑊 ≅ 𝑂𝑊
Statements
1. ∠𝑆 ≅ ∠𝑂; ̅̅̅̅
𝑆𝑂 ⊥ ̅̅̅̅̅
𝑁𝑊
_______________________________________
2. ∠𝑆𝑁𝑊 and ∠𝑂𝑁𝑊 are right angles.
_______________________________________
3. ∠𝑆𝑁𝑊 ≅ ∠𝑂𝑁𝑊
_______________________________________
4. ___________________________________
Reflexive property (same line)
5. ∆𝑆𝑁𝑊 ≅ ∆𝑂𝑁𝑊
_______________________________________
̅̅̅̅̅ ≅ 𝑂𝑊
̅̅̅̅̅
6. 𝑆𝑊
_______________________________________